Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22549626 | C2 | semidirect |
| 4. Q8⋊(C127⋊C8) | C2 | semidirect |
| 6. C8×C127⋊C8 | C2 | semidirect |
| 7. #446×C127 | C2 | semidirect |
| 50. C127⋊C8 | M16 | semidirect |
| 60. C8×C127 | SD16 | semidirect |
| 78. C127 | #1590 | semidirect |
| 79. #446 | D127 | semidirect |
| 138. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523235 | 2 |
| #22549955 | 2 |
| #22549626 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| #22549603 | 2 |
| C8×C127⋊C8 | 2 |
| #446×C127 | 2 |
| #1590 | 127 |